JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The sum of all the integral values of \(p\) such that the equation \(3\sin^2 x + 12\cos x - 3 = p\), \(x \in \mathbb{R}\), has at least one solution, is:
- A \(-54\)
- B \(-60\)
- C \(-75\)
- D \(-84\)
Answer & Solution
Correct Answer
(C) \(-75\)
Step-by-step Solution
Detailed explanation
Given equation: \(3\sin^2 x + 12\cos x - 3 = p\) Substituting \(\sin^2 x = 1 - \cos^2 x\): \(3(1 - \cos^2 x) + 12\cos x - 3 = p\) \(-3\cos^2 x + 12\cos x = p\) Let \(\cos x = t\). Since \(x \in \mathbb{R}\), \(t \in [-1, 1]\). The equation becomes \(p = -3t^2 + 12t\). Let…
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